A classification of unitary highest weight modules of the quantum analogue of the symmetric pair (A(n),A(n-1))

We study the irreducibility and unitarity of highest weight modules of the quantized enveloping algebra associated to sun, 1.. We obtain a classification of these modules analogous to that of wEHWx in the classical context. We also compute all commutation relations between root vectors in Uqsun, 1..